Biological processes take place far away from equilibrium and are of interest to uncover the basic principles governing these phenomena. In this endeavor, molecular transport across channels and transport of cargos by molecular motors are studied. Functioning of a normal cell is contingent upon import of important biomolecules via narrow passage ways called ‘Channels’. Due to entropic barriers the incoming molecules often face hindrance to cross the channels successfully and reach specific locations inside cells. But in real systems the channels utilize special binding sites to accelerate this process. For a set of in-vitro experiments studying molecular flow across channels in presence of the special attractive binding sites, explicit analytical results are derived and they evince how modification of the free energy barrier could achieve quicker translocation; it has been shown that the nature of interactions between molecule and channel, their spatial distribution, strength of interactions and inter-molecular interactions in the channel all contribute to the complex process of translocation. In another study, cargo transport driven by molecular motors is studied. Cells utilize special enzyme molecules called ‘molecular motors’ that convert chemical energy into mechanical motion to transport cargos. Often multiple motors drive transport due to viscous nature of cell medium and other crowding effects in cells. In such systems the extent to which multiple motors share applied load and in turn how they influence the properties of the system is not well understood. From in-vitro measurements pertinent to well-defined structural assemblies and quantitative modeling treatments, it has been shown that the extent to which the motors collectively drive transport depends on the basic biophysical properties of the motors and the loading conditions of the optical trap. Specifically, kinesin motors are seen to negatively cooperate and cooperate positively only under high forces. Further, the microscopic origins of cooperativity is investigated which depend on biochemical interactions of the constituents within the complex and to some extent on mechanical properties. The mechanisms explain how the extent of cooperativity is related to the motor mechanochemistry, how different energy transport modes are manifested during cargo transport and what factors affect cooperative behaviors among multiple motors during transport.